What is BLUE in the context of θ1 in the repaired OCR?

BLUE stands for Best Linear Unbiased Estimator of θ1 in a linear model.

What distributions are mentioned in the repaired page 2 questions?

Distributions such as N(0, σ^2), χ^2_{n-k}, and χ^2_{n-1} are referenced in the context of estimability and model tests.

What is the significance of the matrix (X'X)^{-1} in linear models?

It relates to the variance of the least-squares estimator β̂ in the standard Y = Xβ + e model.

What is the general form of the model used in the page 2 OCR repair?

Models of the form y_{ij} = μ + α_i + β_j + ε_{ij} and y_{ij} = μ + τ_i + ε_{ij} are discussed.

What is the role of residuals e in these MCQ contexts?

Residuals e = Y − Ŷ are used to discuss estimability, distributions (e^T e / σ^2), and related inferential properties.

Statistics Paper II ESISS 2021 MCQ Paper

Name: Statistics Paper II ESISS 2021 MCQ Paper
Creator: ESISS
Keywords: Statistics Paper II, ESISS 2021, MCQ, regression models, estimability, BLUE, Tukey test, SNK test, ANOVA, two-way ANOVA, hypothesis testing, MSE, orthogonality, design of experiments, X'X inverse

Central Government Jobs Other Jobs 2021

Year 2021
Conducted By ESISS
Questions 80
Maximum Marks 200
Duration Two Hours
Languages English & Hindi

Exam Details

Detail	Information
Examination	Statistics Paper II
Year	2021
Conducting Body	ESISS
Paper	Statistics
Subject	Statistics
Duration	Two Hours
Maximum Marks	200
Number of Questions	80
Question Type	Objective (MCQ)

This dataset combines PAGE 1 and PAGE 2 OCR outputs for the Statistics Paper II (ESISS) 2021 exam. Page 1 provides exam metadata: 80 MCQ items, two-hour duration, 200 marks, penalty rules for wrong answers, and general instructions. Page 2 presents a repaired set of objective questions focusing on regression models, estimability, and linear model theory. The OCR-repaired items cover two-way and single-factor models, residual distributions, and linear combinations of parameters, along with topics on estimability, BLUE, chi-square distributions, and multiple comparison procedures (Tukey and SNK). The combined material informs SEO metadata, structured QA, and related topics for exam-prep content.

Major Topics Covered

Regression models
Two-way ANOVA
Estimability
Linear models
Design of Experiments
ANOVA
Residuals
Matrix algebra in statistics
X'X inverse
BLUE
Hypothesis testing
Multiple comparisons
Tukey's test
Student-Newman-Keuls
Type I error
MSE
Chi-square distribution
Parameter estimation
Unbalanced designs
Orthogonality

Why This Paper is Important

Useful for Statistics Paper II preparation
Helps understand the latest exam pattern
Useful for practice and self-assessment
Covers frequently asked General Studies topics
Helpful for analysing question trends

Related Resources

Instructions

THIS TEST BOOKLET DOES NOT HAVE ANY UNPRINTED OR TORN OR MISSING PAGES OR ITEMS, ETC.
IF SO, GET IT REPLACED BY A COMPLETE TEST BOOKLET.
Please note that it is the candidate's responsibility to encode and fill in the Roll Number and Test
Booklet Series Code A, B, C or D carefully and without any omission or discrepancy at the appropriate places in the OMR Answer Sheet.
Any omission/discrepancy will render the Answer Sheet liable for rejection.
You have to enter your Roll Number on the Test Booklet in the Box provided alongside.
DO NOT write anything else on the Test Booklet.
This Test Booklet contains 80 items (questions).
Each item comprises four responses (answers).
will select the response which you want to mark on the Answer Sheet.
In case you feel that there is more than one correct response, mark the response which you consider the best.
In any case, choose ONLY ONE response for each item.
You have to mark all your responses ONLY on the separate Answer Sheet provided.
Before you proceed to mark in the Answer Sheet the response to various items in the Test Booklet,
you have to fill in some particulars in the Answer Sheet as per instructions sent to you with your Admission Certificate.
After you have completed filling in all your responses on the Answer Sheet and the examination has concluded, you should hand over to the Invigilator only the Answer Sheet.
You are permitted to take away with you the Test Booklet.
Sheets for rough work are appended in the Test Booklet at the end.
THERE WILL BE PENALTY FOR WRONG ANSWERS MARKED BY A CANDIDATE IN THE OBJECTIVE TYPE QUESTION PAPERS.

Questions (page 2)

Q1. ESISS Exam, 2021 Consider the model y_ij = μ + α_i + β_j + \varepsilon_ii, In general regression model 4. 1. Y_{n× 1} = X_{n× k}β_{k× 1} + \varepsilon_{n× 1}. Further \varepsilon is N(0, σ^2 I). i = 1, 2; j = 1,

Q2.

(a) For which one of the following The n × 1 vector of ordinary residuals is choices of λ', the function λ' β where denoted by e = Y - \hatY. The distribution of (eⁱe)/(σ^2) β' = (μ, α_1, α_2, β_1, β_2) is not estimable ? (1, 1, 0, 1, 0) is (0, 0, 0, -1, 1)
(b) N(0, σ^2 \rho) (a)
(c) (0, -1, 1, 0, 0) N(Xβ, σ^2) (b) (1, 1, 1, 1, 1)
(d) \chi²_\rm n-k
(c) For the model y_ij = μ + \tau_i + \varepsilon_ij, i = 1, 2; j = 1, 2; 2. \chi²_n-1 (d) consider the following statements:
5. Consider a model μ + \tau₁ is estimable.
1. Y₁ = A + B + C + D + e₁; \tau₁ + \tau₂ is estimable.
2. Y₂ = A + C - B - D + e₂; Which of the above statements is/are correct? Y₃ = A + B - C - D + e₃; Y₄ = A + D - B - C + e₄. (a) 1 only (b) 2 only If this model is equivalent to Y = Xβ + e, then the matrix (X'X)^-1 is equal to
(c) Both 1 and 2 (d) Neither 1 nor 2 (a) 1/3 I 4 (b) 1/2 I₄ Let X_i, Y_i and Z_i; i = 1, 2, 3 be nine
3. independent observations with common
(c) 1/5 I₄ variance σ^2, and E(X_i) = θ_1, E(Y_i) = θ_2, (d) 1/4 I₄ E(Z_i) = θ_1 - θ_2; i = 1, 2,
3. If X = ∑_i=1³ x_i, Y = ∑_i=1³ y_i and Z = ∑_i=1³ z_i, then the
6. Consider the following statements: BLUE of θ_1 is given by
1. Tukey's test of multiple comparisons (a) 1/9 [2X + Y - Z] reduces the Type-I error in the test.
2. Student-Newman-Keuls test uses stepwise procedure. (b) 1/9 [X + 2Y - Z] Which of the above statements is/are correct? (a) 1 only
(c) 1/9 [X + 2Y - 2Z] 2 only (b)
(c) Both 1 and 2 1/9 [X + 3Y - 2Z] (d) (d) Neither 1 nor 2 (2 - A)

Q3. Let X_i, Y_i and Z_i; i = 1, 2, 3 be nine independent observations with common variance σ^2, and E(X_i) = θ1, E(Y_i) = θ2, E(Z_i) = θ1 - θ2; i = 1, 2, 3. If X = ∑ x_i, Y = ∑ y_i and Z = ∑ z_i, then the

(a) 1/3 I₄
(b) 1/2 I₄
(c) 1/5 I₄
(d) 1/4 I₄

Q4. Consider the following statements: BLUE of θ1 is given by

(a) 1/3 I₄
(b) 1/2 I₄
(c) 1/5 I₄
(d) 1/4 I₄

Q5. 6. Consider the following statements: BLUE of θ1 is given by

(a) 1/3 I₄
(b) 1/2 I₄
(c) 1/5 I₄
(d) 1/4 I₄

Q6. 6. Consider the following statements: Tukey's test of multiple comparisons reduces the Type-I error in the test; SNK test uses a stepwise procedure. Which of the above statements is/are correct?

(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

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Frequently asked questions

What is the duration of Statistics Paper II (ESISS) 2021?

Two hours.

How many questions are in Statistics Paper II?

200 marks with 80 items (questions) in the test booklet, as indicated by the exam instructions.

What is the marking scheme mentioned in the paper?

All items carry equal marks; there is a penalty for wrong answers (one-third of the marks for that question). No penalty for unattempted questions.

What topics are covered in the repaired page 2 objectives?

Topics include regression models, estimability of linear combinations, BLUE (best linear unbiased estimator), and multiple comparison procedures (Tukey and SNK).

What does estimable mean in the context of linear models?

An estimable quantity is a linear combination of parameters that can be unbiasedly estimated from the data.

What are Tukey's and SNK tests used for?

They are methods for multiple comparisons to control Type I error in post-hoc analyses after ANOVA.

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